1. B. T remains the same and vmax doubles.
Q14.1
An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed vmax?
A. T and vmax both double.
B. T remains the same and vmax doubles.
C. T and vmax both remain the same.
D. T doubles and vmax remains the same.
E. T remains the same and vmax increases by a factor of
Answer: B

2. A14.1
An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed vmax?
A. T and vmax both double.
B. T remains the same and vmax doubles.
C. T and vmax both remain the same.
D. T doubles and vmax remains the same.
E. T remains the same and vmax increases by a factor of

3. E. Two of the above are tied for most negative velocity.
Q14.2
This is an x-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
E. Two of the above are tied for most negative velocity.
Answer: A

4. A14.2
This is an x-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
E. Two of the above are tied for most negative velocity.

5. E. Two of the above are tied for most negative acceleration.
Q14.3
This is an x-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative acceleration ax?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
E. Two of the above are tied for most negative acceleration.
Answer: D

6. A14.3
This is an x-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative acceleration ax?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
E. Two of the above are tied for most negative acceleration.

7. E. Two of the above are tied for most negative displacement.
Q14.4
This is an ax-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative displacement x?
A. t = 0.10 s
B. t = 0.15 s
C. t = 0.20 s
D. t = 0.25 s
E. Two of the above are tied for most negative displacement.
Answer: B

8. A14.4
This is an ax-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative displacement x?
A. t = 0.10 s
B. t = 0.15 s
C. t = 0.20 s
D. t = 0.25 s
E. Two of the above are tied for most negative displacement.

9. E. Two of the above are tied for most negative velocity.
Q14.5
This is an ax-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx?
A. t = 0.10 s
B. t = 0.15 s
C. t = 0.20 s
D. t = 0.25 s
E. Two of the above are tied for most negative velocity.
Answer: A

10. A14.5
This is an ax-t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx?
A. t = 0.10 s
B. t = 0.15 s
C. t = 0.20 s
D. t = 0.25 s
E. Two of the above are tied for most negative velocity.

11. E. Two of the above are tied for greatest potential energy.
Q14.6
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. At which of the following times is the potential energy of the spring the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. Two of the above are tied for greatest potential energy.
Answer: D

12. A14.6
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. At which of the following times is the potential energy of the spring the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. Two of the above are tied for greatest potential energy.

13. E. Two of the above are tied for greatest kinetic energy.
Q14.7
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. At which of the following times is the kinetic energy of the object the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. Two of the above are tied for greatest kinetic energy.
Answer: B

14. A14.7
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. At which of the following times is the kinetic energy of the object the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. Two of the above are tied for greatest kinetic energy.

15. Q14.8
To double the total energy of a mass-spring system oscillating in simple harmonic motion, the amplitude must increase by a factor of
A. 4. B.
C. 2. D. E.
Answer: D

16. A14.8
To double the total energy of a mass-spring system oscillating in simple harmonic motion, the amplitude must increase by a factor of
A. 4. B.
C. 2. D. E.

17. A. becomes four times greater. B. becomes twice as great.
Q14.9
A simple pendulum consists of a point mass suspended by a massless, unstretchable string. If the mass is doubled while the length of the string remains the same, the period of the pendulum
A. becomes four times greater.
B. becomes twice as great.
C. becomes greater by a factor of
D. remains unchanged.
E. decreases.
Answer: D

18. A14.9
A simple pendulum consists of a point mass suspended by a massless, unstretchable string. If the mass is doubled while the length of the string remains the same, the period of the pendulum
A. becomes four times greater.
B. becomes twice as great.
C. becomes greater by a factor of
D. remains unchanged.
E. decreases.

19. A. when it is at maximum positive displacement.
Q14.10
The force on a damped oscillator is Fx = –kx – bvx. During its motion, the oscillator loses mechanical energy most rapidly
A. when it is at maximum positive displacement.
B. when it is at maximum negative displacement.
C. when it is passing through the equilibrium position.
D. when it is at either maximum positive or maximum negative displacement.
E. Misleading question—the oscillator loses mechanical energy at the same rate at all times during the motion.
Answer: C

20. A14.10
The force on a damped oscillator is Fx = –kx – bvx. During its motion, the oscillator loses mechanical energy most rapidly
A. when it is at maximum positive displacement.
B. when it is at maximum negative displacement.
C. when it is passing through the equilibrium position.
D. when it is at either maximum positive or maximum negative displacement.
E. Misleading question—the oscillator loses mechanical energy at the same rate at all times during the motion.

21. Q-RT14.1
Three identical oscillators have the same amplitude A and the same angular frequency All three oscillate in simple harmonic motion given by x = A cos The three oscillators have different phase angles however. Rank the three oscillators in order of their displacement x at t = 0, from most positive to most negative. A. B. C.
Answer: ABC

22. A-RT14.1
Three identical oscillators have the same amplitude A and the same angular frequency All three oscillate in simple harmonic motion given by x = A cos The three oscillators have different phase angles however. Rank the three oscillators in order of their displacement x at t = 0, from most positive to most negative. A. B. C.
Answer: ABC

23. Q-RT14.2
Three identical oscillators have the same amplitude A and the same angular frequency All three oscillate in simple harmonic motion given by x = A cos The three oscillators have different phase angles however. Rank the three oscillators in order of their velocity vx at t = 0, from most positive to most negative. A. B. C.
Answer: CAB

24. A-RT14.2
Three identical oscillators have the same amplitude A and the same angular frequency All three oscillate in simple harmonic motion given by x = A cos The three oscillators have different phase angles however. Rank the three oscillators in order of their velocity vx at t = 0, from most positive to most negative. A. B. C.
Answer: CAB